Suppose you are concerned with determining what the most visited parks in a city are. One idea is to take a momentary snapshot: to see how many people are this moment in park A, how many are in park B and so on. Another idea is to look at one individual (or few of them) and to follow him for a certain period of time, e.g. a year. Then, you observe how often the individual is going to park A, how often he is going to park B and so on.
Thus, you obtain two different results: one statistical analysis over the entire ensemble of people at a certain moment in time, and one statistical analysis for one person over a certain period of time. The first one may not be representative for a longer period of time, while the second one may not be representative for all the people. The idea is that an ensemble is ergodic if the two types of statistics give the same result. Many ensembles, like the human populations, are not ergodic.
The importance of ergodicity becomes manifest when you think about how we all infer various things, how we draw some conclusion about something while having information about something else. For example, one goes once to a restaurant and likes the fish and next time he goes to the same restaurant and orders chicken, confident that the chicken will be good. Why is he confident? Or one observes that a newspaper has printed some inaccurate information at one point in time and infers that the newspaper is going to publish inaccurate information in the future. Why are these inferences ok, while others such as “more crimes are committed by black persons than by white persons, therefore each individual black person is not to be trusted” are not ok?
The answer is that the ensemble of articles published in a newspaper is more or less ergodic, while the ensemble of black people is not at all ergodic. If one searches how many mistakes appear in an entire newspaper in one issue, and then searches how many mistakes one news editor does over time, one finds the two results almost identical (not exactly, but nonetheless approximately equal). However, if one takes the number of crimes committed by black people in a certain day divided by the total number of black people, and then follows one random-picked black individual over his life, one would not find that, e.g. each month, this individual commits crimes at the same rate as the crime rate determined over the entire ensemble. Thus, one cannot use ensemble statistics to properly infer what is and what is not probable that a certain individual will do.
If neoliberalism were anything other than a self-serving con, whose gurus and think tanks were financed from the beginning by some of the richest people on earth … its apostles would have demanded, as a precondition for a society based on merit, that no one should start life with the unfair advantage of inherited wealth or economically-determined education. But they never believed in their own doctrine. Enterprise, as a result, quickly gave way to rent.
All this is ignored, and success or failure in the market economy are ascribed solely to the efforts of the individual. The rich are the new righteous, the poor are the new deviants, who have failed both economically and morally, and are now classified as social parasites.
The market was meant to emancipate us, offering autonomy and freedom. Instead it has delivered atomisation and loneliness. The workplace has been overwhelmed by a mad, Kafka-esque infrastructure of assessments, monitoring, measuring, surveillance and audits, centrally directed and rigidly planned, whose purpose is to reward the winners and punish the losers. It destroys autonomy, enterprise, innovation and loyalty and breeds frustration, envy and fear.
Structural econometrics aims to infer causes from probabilities, inferred from sample data generated in non-experimental settings. Arguably, it is the most ambitious part of econometrics. It aims to identify economic structures, robust parts of the economy to which interventions can be made to bring about desirable events. This part of econometrics is distinguished from forecasting econometrics in its attempt to capture something of the ‘real’ economy in the hope of allowing policy makers to act on and control events …
By making many strong background assumptions, the deductivist [the conventional logic of structural econometrics] reading of the regression model allows one — in principle — to support a structural reading of the equations and to support many rich causal claims as a result. Here, however, the difficulty is that of finding good evidence for many of the assumptions on which the approach rests. It seems difficult to believe, even in cases where we have good background economic knowledge, that the background information will be sufficiently to do the job that the deductivist asks of it. As a result, the deductivist approach may be difficult to sustain, at least in economics.
The difficulties in providing an evidence base for the deductive approach show just how difficult it is to warrant such strong causal claims. In short, as might be expected there is a trade-off between the strength of causal claims we would like to make from non-experimental data and the possibility of grounding these in evidence. If this conclusion is correct — and an appropriate elaboration were done to take into account the greater sophistication of actual structural econometric methods — then it suggests that if we want to do evidence-based structural econometrics, then we may need to be more modest in the causal knowledge we aim for. Or failing this, we should not act as if our causal claims — those that result from structural econometrics — are fully warranted by the evidence and we should acknowledge that they rest on contingent, conditional assumptions about the economy and the nature of causality.
Ever since the Enlightenment various economists had been seeking to mathematise the study of the economy. In this, at least prior to the early years of the twentieth century, economists keen to mathematise their discipline felt constrained in numerous ways, and not least by pressures by (non-social) natural scientists and influential peers to conform to the ‘standards’ and procedures of (non-social) natural science, and thereby abandon any idea of constructing an autonomous tradition of mathematical economics. Especially influential, in due course, was the classical reductionist programme, the idea that all mathematical disciplines should be reduced to or based on the model of physics, in particular on the strictly deterministic approach of mechanics, with its emphasis on methods of infinitesimal calculus …
However, in the early part of the twentieth century changes occurred in the inter-pretation of the very nature of mathe-matics, changes that caused the classical reductionist programme itself to fall into disarray. With the development of relativity theory and especially quantum theory, the image of nature as continuous came to be re-examined in particular, and the role of infinitesimal calculus, which had previously been regarded as having almost ubiquitous relevance within physics, came to be re-examined even within that domain.
The outcome, in effect, was a switch away from the long-standing emphasis on mathematics as an attempt to apply the physics model, and specifically the mechanics metaphor, to an emphasis on mathematics for its own sake.
Mathematics, especially through the work of David Hilbert, became increasingly viewed as a discipline properly concerned with providing a pool of frameworks for possible realities. No longer was mathematics seen as the language of (non-social) nature, abstracted from the study of the latter. Rather, it was conceived as a practice concerned with formulating systems comprising sets of axioms and their deductive consequences, with these systems in effect taking on a life of their own. The task of finding applications was henceforth regarded as being of secondary importance at best, and not of immediate concern.
This emergence of the axiomatic method removed at a stroke various hitherto insurmountable constraints facing those who would mathematise the discipline of economics. Researchers involved with mathematical projects in economics could, for the time being at least, postpone the day of interpreting their preferred axioms and assumptions. There was no longer any need to seek the blessing of mathematicians and physicists or of other economists who might insist that the relevance of metaphors and analogies be established at the outset. In particular it was no longer regarded as necessary, or even relevant, to economic model construction to consider the nature of social reality, at least for the time being. Nor, it seemed, was it possible for anyone to insist with any legitimacy that the formulations of economists conform to any specific model already found to be successful elsewhere (such as the mechanics model in physics). Indeed, the very idea of fixed metaphors or even interpretations, came to be rejected by some economic ‘modellers’ (albeit never in any really plausible manner).
The result was that in due course deductivism in economics, through morphing into mathematical deductivism on the back of developments within the discipline of mathematics, came to acquire a new lease of life, with practitioners (once more) potentially oblivious to any inconsistency between the ontological presuppositions of adopting a mathematical modelling emphasis and the nature of social reality. The consequent rise of mathematical deductivism has culminated in the situation we find today.
Coupled with downright incompetence in statistics, we often find the syndrome that I have come to call statisticism: the notion that computing is synonymous with doing research, the naïve faith that statistics is a complete or sufficient basis for scientific methodology, the superstition that statistical formulas exist for evaluating such things as the relative merits of different substantive theories or the “importance” of the causes of a “dependent variable”; and the delusion that decomposing the covariations of some arbitrary and haphazardly assembled collection of variables can somehow justify not only a “causal model” but also, praise a mark, a “measurement model.” There would be no point in deploring such caricatures of the scientific enterprise if there were a clearly identifiable sector of social science research wherein such fallacies were clearly recognized and emphatically out of bounds.
Dudley Duncan: Notes on Social Measurement
Let’s say we have a stationary process. That does not guarantee that it is also ergodic. The long-run time average of a single output function of the stationary process may not converge to the expectation of the corresponding variables — and so the long-run time average may not equal the probabilistic (expectational) average.
Say we have two coins, where coin A has a probability 1/2 of coming up heads, and coin B has a probability of 1/4 of coming up heads. We pick either of these coins with a probability of 1/2 and then toss the chosen coin over and over again. Now let H1, H2, … be either one or zero as the coin comes up heads or tales. This “process” is obviously stationary, but the time averages — [H1 + ... + Hn]/n — converges to 1/2 if coin A is chosen, and 1/4 if coin B is chosen. Both these time averages has probability of 1/2 and so their expectational average is 1/2 x 1/2 + 1/2 x 1/4 = 3/8, which obviously is not equal to 1/2 or 1/4. The time averages depend on which coin you happen to choose, while the probabilistic (expectational) average is calculated for the whole “system” consisting of both coin A and coin B.
Till A.L. — som lyste upp tillvaron under tre år på Linnéskolan
I’ve never yet been able to understand why the economics profession was/is so impressed by the Arrow-Debreu results. They establish that in an extremely abstract model of an economy, there exists a unique equilibrium with certain properties. The assumptions required to obtain the result make this economy utterly unlike anything in the real world. In effect, it tells us nothing at all. So why pay any attention to it? The attention, I suspect, must come from some prior fascination with the idea of competitive equilibrium, and a desire to see the world through that lens, a desire that is more powerful than the desire to understand the real world itself. This fascination really does hold a kind of deranging power over economic theorists, so powerful that they lose the ability to think in even minimally logical terms; they fail to distinguish necessary from sufficient conditions, and manage to overlook the issue of the stability of equilibria.
Almost a century and a half after Léon Walras founded neoclassical general equilibrium theory, economists still have not been able to show that markets move economies to equilibria.
We do know that — under very restrictive assumptions — equilibria do exist, are unique and are Pareto-efficient. After reading Buchanan’s article one however has to ask oneself — what good does that do?
As long as we cannot show, except under exceedingly special assumptions, that there are convincing reasons to suppose there are forces which lead economies to equilibria — the value of general equilibrium theory is negligible. As long as we cannot really demonstrate that there are forces operating — under reasonable, relevant and at least mildly realistic conditions — at moving markets to equilibria, there cannot really be any sustainable reason for anyone to pay any interest or attention to this theory.
A stability that can only be proved by assuming “Santa Claus” conditions is of no avail. Most people do not believe in Santa Claus anymore. And for good reasons. Santa Claus is for kids, and general equilibrium economists ought to grow up.
Continuing to model a world full of agents behaving as economists — “often wrong, but never uncertain” — and still not being able to show that the system under reasonable assumptions converges to equilibrium (or simply assume the problem away) is a gross misallocation of intellectual resources and time.
And then, of course, there is Sonnenschein-Mantel-Debreu!
So what? Why should we care about Sonnenschein-Mantel-Debreu?
Because Sonnenschein-Mantel-Debreu ultimately explains why New Classical, Real Business Cycles, Dynamic Stochastic General Equilibrium (DSGE) and “New Keynesian” microfounded macromodels are such bad substitutes for real macroeconomic analysis!
These models try to describe and analyze complex and heterogeneous real economies with a single rational-expectations-robot-imitation-representative-agent. That is, with something that has absolutely nothing to do with reality. And — worse still — something that is not even amenable to the kind of general equilibrium analysis that they are thought to give a foundation for, since Hugo Sonnenschein (1972) , Rolf Mantel (1976) and Gerard Debreu (1974) unequivocally showed that there did not exist any condition by which assumptions on individuals would guarantee neither stability nor uniqueness of the equlibrium solution.
Opting for cloned representative agents that are all identical is of course not a real solution to the fallacy of composition that the Sonnenschein-Mantel-Debreu theorem points to. Representative agent models are — as I have argued at length here — rather an evasion whereby issues of distribution, coordination, heterogeneity — everything that really defines macroeconomics — are swept under the rug.
Instead of real maturity, we see that general equilibrium theory possesses only pseudo-maturity. For the description of the economic system, mathematical economics has succeeded in constructing a formalized theoretical structure, thus giving an impression of maturity, but one of the main criteria of maturity, namely, verification, has hardly been satisfied. In comparison to the amount of work devoted to the construction of the abstract theory, the amount of effort which has been applied, up to now, in checking the assumptions and statements seems inconsequential.